Electrophotography is a useful process for printing images on a receiver (or “imaging substrate”), such as a piece or sheet of paper or another planar medium, glass, fabric, metal, or other objects as will be described below. In this process, an electrostatic latent image is formed on a photoreceptor by uniformly charging the photoreceptor and then discharging selected areas of the uniform charge to yield an electrostatic charge pattern corresponding to the desired image (a “latent image”).
After the latent image is formed, charged toner particles are brought into the vicinity of the photoreceptor and are attracted to the latent image to develop the latent image into a visible image. Note that the visible image may not be visible to the naked eye depending on the composition of the toner particles (e.g., clear toner).
After the latent image is developed into a visible image on the photoreceptor, a suitable receiver is brought into juxtaposition with the visible image. A suitable electric field is applied to transfer the toner particles of the visible image to the receiver to form the desired print image on the receiver. The imaging process is typically repeated many times with reusable photoreceptors.
The receiver is then removed from its operative association with the photoreceptor and subjected to heat or pressure to permanently fix (“fuse”) the print image to the receiver. Plural print images, e.g., of separations of different colors, are overlaid on one receiver before fusing to form a multi-color print image on the receiver.
Electrophotographic (EP) printers typically transport the receiver past the photoreceptor to form the print image. The direction of travel of the receiver is referred to as the slow-scan, process, or in-track direction. This is typically the vertical (Y) direction of a portrait-oriented receiver. The direction perpendicular to the slow-scan direction is referred to as the fast-scan, cross-process, or cross-track direction, and is typically the horizontal (X) direction of a portrait-oriented receiver. “Scan” does not imply that any components are moving or scanning across the receiver; the terminology is conventional in the art.
Various components, such as belts and drums, used in the electrophotographic process can have mechanical or electrical characteristics that result in periodic objectionable nonuniformities in print images, such as streaks (extending in-track) or bands (extending cross-track). For example, drums can experience runout: they can be elliptical rather than circular in cross-section, or mounted slightly off-center, so that the radius of the drum at a particular angle with the horizontal varies over time. Belts can have thicknesses that vary across their widths (cross-track) or along their lengths (in-track). Damped springs for mounting components can experience periodic vibrations, causing the spacing between the mounted components to change over time. These variations are generally periodic in nature, that is, each variation cycles through various magnitudes repeatedly in sequence, at a characteristic and generally fixed frequency.
Various schemes have been proposed for correcting the nonuniformities resulting from these mechanical variations. U.S. Pat. No. 7,058,325 to Hamby et al. deposits a test patch, measures its density, and corrects using a feedback or feed-forward control routine. U.S. Patent Publication No. 2008/0226361 by Tomita et al. describes measuring multiple patterns, each containing multiple rows of toner, possibly set at different angles on the page, and combining the measurement results to determine image adjustments. U.S. Pat. No. 7,755,799 to Paul et al. also measures test patches, and uses a defect once-around signal to synchronize the measurements to the rotation of the drum. The once-around signal is derived from an optical sensor monitoring the drum's position. Paul describes that the phase of a periodic banding defect (a non-uniformity extending cross-track) is difficult to measure because, unlike frequency, it varies from page to page.
The various schemes discussed above require additional sensors or calculations on low-amplitude, noisy data to determine the phase of banding defects and other periodic nonuniformities. Moreover, multiple components in a printer can have individual nonuniformities, which interact with each other. This results in significant noise in measured density data. There is an ongoing need, therefore, for an improved way of characterizing the periodic nonuniformities in an electrophotographic printer.